Limits, applicability and generalizations of the Landauer's erasure principle

Almost sixty years since Landauer linked the erasure of information with an increase of entropy, his famous erasure principle and byproducts like reversible computing are still subjected to debates in the scientific community. In this work we use the Liouville theorem to establish three different types of the relation between manipulation of information by a logical gate and the change of its physical entropy, corresponding to three types of the final state of environment. A time-reversible relation can be established when the final states of environment corresponding to different logical inputs are macroscopically distinguishable, showing a path to reversible computation and erasure of data with no entropy cost. A weak relation, giving the entropy change of $k \ln 2$ for an erasure gate, can be deduced without any thermodynamical argument, only requiring the final states of environment to be macroscopically indistinguishable. The common strong relation that links entropy cost to heat requires the final states of environment to be in a thermal equilibrium. We argue in this work that much of the misunderstanding around the Landauer's erasure principle stems from not properly distinguishing the limits and applicability of these three different relations. Due to new technological advances, we emphasize the importance of taking into account the time-reversible and weak types of relation to link the information manipulation and entropy cost in erasure gates beyond the considerations of environments in thermodynamic equilibrium.Comment: 26 pages, 3 figure

On the origin of ambiguity in efficient communication

This article studies the emergence of ambiguity in communication through the concept of logical irreversibility and within the framework of Shannon's information theory. This leads us to a precise and general expression of the intuition behind Zipf's vocabulary balance in terms of a symmetry equation between the complexities of the coding and the decoding processes that imposes an unavoidable amount of logical uncertainty in natural communication. Accordingly, the emergence of irreversible computations is required if the complexities of the coding and the decoding processes are balanced in a symmetric scenario, which means that the emergence of ambiguous codes is a necessary condition for natural communication to succeed.Comment: 28 pages, 2 figure

Quantum memories and Landauer's principle

Two types of arguments concerning (im)possibility of constructing a scalable, exponentially stable quantum memory equipped with Hamiltonian controls are discussed. The first type concerns ergodic properties of open Kitaev models which are considered as promising candidates for such memories. It is shown that, although the 4D Kitaev model provides stable qubit observables, the Hamiltonian control is not possible. The thermodynamical approach leads to the new proposal of the revised version of Landauer's principle and suggests that the existence of quantum memory implies the existence of the perpetuum mobile of the second kind. Finally, a discussion of the stability property of information and its implications is presented.Comment: 10 pages, no figures, lecture given at 46 School of Theoretical Physics, Ladek, Poland, February 201